Certain aspects of the (linear and nonlinear) stability of sheared relativistic (slab) jets are analyzed. The linear problem has been solved for a wide range of jet models well inside the ultrarelativistic domain (flow Lorentz factors up to 20, specific internal energies approximately 60c2). As a distinct feature of our work, we have combined the analytical linear approach with high-resolution relativistic hydrodynamical simulations, which has allowed us (i) to identify, in the linear regime, resonant modes specific to the relativistic shear layer, (ii) to confirm the result of the linear analysis with numerical simulations, and (iii) more interestingly, to follow the instability development through the nonlinear regime. We find that very-high-order reflection modes with dominant growth rates can modify the global, long-term stability of the relativistic flow. We discuss the dependence of these resonant modes on the jet flow Lorentz factor and specific internal energy and on the shear-layer thickness. The results could have potential applications in the field of extragalactic relativistic jets.
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